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Monoliths as Biocatalytic Reactors: Smart Gas-Liquid Contacting for Process Intensification Michiel T. Kreutzer,* Freek Kapteijn, and Jacob A. Moulijn Reactor and Catalysis Engineering, DelftChemTech, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands
Sirous Ebrahimi, Robbert Kleerebezem, and Mark C. M. van Loosdrecht Environmental Technology, Kluyver Laboratory for Biotechnology, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands
In this paper, the advantages and disadvantages of using segmented flow in microchannels to intensify biocatalytic processes are discussed. We consider both suspended cell cultures and immobilized enzymes. Once bubbles are formed in microchannels, they can no longer coalesce and, hence, no energy is required to break up larger bubbles. As a result, the same gas-liquid mass-transfer behavior can be obtained at an order of magnitude lower power input. The gasliquid-solid mass transfer, i.e., to a catalyst on the channel walls, improves with decreasing energy input, allowing the combined reduction of power input and reactor size. These findings are supported by a scaling analysis based on the pressure drop work of Kreutzer et al.1 and the mass-transfer work of Van Baten and Krishna.2 For the practical application of monoliths for liquid-phase cell cultures, the stability of a downflow monolith reactor with respect to clogging by biofilm was investigated experimentally. The results indicated that, as long as flushing out of the suspended cells was prevented, stable operation was possible. Introduction Honeycomb monoliths are structured catalyst supports of parallel, straight capillary channels. Nowadays, they are widely used for the catalytic exhaust converter in the automobile industry and in end-of-pipe gas cleaning. The gas-only application of monoliths stems from the fact that the pressure drop is low: using the surface area of the catalyst as a criterion, the pressure drop in monoliths is an order of magnitude lower than in random packed beds. The channels are ∼1 mm in diameter, and on the wall (∼100 µm), a washcoat of catalytic material (∼50 µm) is applied. In the past decade, monoliths have been increasingly considered for liquid-phase reactions,3-9 mainly in various forms of a loop configuration. In our department, the monolith packings have been applied for a host of gas-liquid-solid (G/L/S) applications. Briefly, we have obtained hydrogenation rates for R-methylstyrene that were orders of magnitude higher than in typical packed beds,10 and we have obtained selectivities in the A f B f C hydrogenation of benzaldehyde that were similar to values obtained in fine powder slurry reactors.11 Monoliths have been used in biotechnological applications using immobilized enzymes12 and in air-lift biofilm reactors.13 Recently, we have used several carbon-based techniques to prepare monoliths with immobilized enzymes,14 and these structures have been used to catalyze several model reactions. The high mass-transfer characteristics were obtained in plug-flow15 conditions and at minimal or even zero pressure drop.16,17 The last observation is unlike normal multiphase reactor behavior: quite generally, mechan* Corresponding author. Tel.: +31 15 278 90 84. Fax: +31 15 278 50 06. E-mail:
[email protected].
ical energy is used to overcome mass-transfer limitations, whether by using smaller particles in fixed beds at the expense of pressure drop or by using higher stirrer speeds or gas throughput in slurry systems. As a result, most of the equipment heralded in process intensification not only intensifies chemical conversion per unit volume but also intensifies the mechanical energy dissipation per unit volume, beating the fluids, in some way or other, into a high contact area and thin boundary layers. The first aim of this contribution is to investigate, quite generally, why monoliths are able to compete on mass-transfer performance with such devices at orders-of-magnitude lower power inputs. The second aim of this paper is to explore the feasibility of using these monoliths to intensify biochemical conversions. Most of the gas-liquid (G/L) applications of monoliths have used a heterogeneous catalyst (whether supported noble metals or immobilized enzymes) on the channel walls. In this paper, we also consider the use of monoliths without a catalyst on the walls in gas-liquid applications, i.e., homogeneously catalyzed liquid-phase reactions. The fluid mechanics of the system do not change appreciably by letting the reaction take place in the liquid bulk as opposed to in a washcoat layer, and it is interesting to consider such reactions in a discussion of mass-transfer and power-input requirements. Of course, the mass-transfer behavior does change by changing the location where the reaction takes place, and we will discuss gas-liquid reactors and gas-liquid-solid reactors separately. One of the gas-liquid applications that would benefit from intensification at a low mechanical energy input is industrial fermentation, which frequently is masstransfer limited in air-lifts, bubble columns, and gently stirred tanks. High-shear mechanical energy tends to
10.1021/ie050286m CCC: $30.25 © 2005 American Chemical Society Published on Web 06/02/2005
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kill the cells, and the mechanical intensifiers that work just fine for catalyst powders are much less attractive for fermentations. Fermentations are generally performed at low pressure in very large reactors, even by chemical engineering standards, and reduction of energy costs is often desired. Besides industrial fermentation processes, environmental processes involving gas-liquid mass transfer and microbial conversion exist for which the same arguments apply. Examples include aerobic wastewater treatment and biotechnological gas treatment processes such as those developed for NOx and SOx removal from flue gases.18,19 A practical matter that must be resolved is the clogging of monoliths while a cell culture flows through it. In this respect, the automotive car catalyst is far from optimal: the micron-sized macropores of the cordierite substrate are ideal anchors for cells to attach to the wall and to form the biofilm that eventually blocks the entire channels. Also, the channels are very small and the large available wall surface area provides many of these anchor points per unit channel volume. In this contribution, we report some initial tests in a pilot bioreactor, and we indicate at which conditions clogging does or does not occur. Power Required for Gas-Liquid Dispersion Turbulent Contactors. A comparison of different gas-liquid contactors best starts with exploring the amount of energy that is needed to generate interfacial area. In conventional turbulent contactors, the bubble size is determined by bubble breakup and coalescence. In essence, one can set up a balance between (1) surface tension, which resists the deformation of the convex bubble shape that leads to bubble breakup, and (2) turbulent eddies, which batter away at the interface. The ratio between these stresses gives a Weber-number criterion for bubble breakup,20
FLu(l)2 ∼ γ/dB
(1)
in which u(l)2 can be estimated from the power dissipated per unit volume in eddies of similar length scale as the bubble scale.21 Such an analysis leads to
dB ∼
γ2/5 (P/V)2/5FL1/5
(2)
which indicates that the interfacial area is proportional to (P/V)0.4. Generally, for the group kLa, a slightly higher exponent with respect to power input is observed, which indicates that the mass-transfer coefficient is a mild function of the turbulence intensity surrounding the bubble.22 Naturally, a higher bubble holdup increases the bubble surface area, and correlations of the following type are widely used
k La ∼
() ( ) P V
0.65
uG,s V
a
(3)
in which (uG,s/V) accounts for the gas holdup with the constant a typically in the range 0.2-0.3. It should be stressed here that correlations such as eq 3 are more firmly rooted in turbulence theory than their first empirical appearance suggests. The power of the eddies mainly breaks up bubbles into smaller ones (∼(P/V)0.4) but also reduces the boundary layer surrounding the
Figure 1. Computed flow of a bubble in a capillary. A lubricating thin liquid layer (dark gray) persists on the wall. Liquid between the slugs (light gray) circulates. Kreutzer et al.1 have reported the numerical details.
bubbles (∼(P/V)0.25), and the combination of these effects leads to eq 3. The proportionality constant for eq 3 varies from equipment to equipment and, of course, is fluid-property dependent. For oxygen transfer to a clean aqueous medium, a value of 1 × 10-3 gives values of the right order of magnitude, kLa ∼ 0.05 s-1 at (P/V) ) 103 W/m3 and kLa ∼ 0.2 s-1 at (P/V) ) 104 W/m3; see for example, Linek et al.23 or Schlu¨ter and Deckwer.24 The coupling of power dissipation and mass transfer hinders the achievement of the goals of process intensification: while high mass-transfer rates may be achieved to reduce the reactor size, the auxiliary equipment needed to achieve the vigorous contactingsbe it a stirrer, pump, venturi ejector, or compressorswill grow in size and, perhaps more importantly, will grow in energy requirements. For the intensification of hazardous processes where the minimization of toxic or explosive inventory is most important, the energy costs are not driving the process intensification. But, for large scale processes where operating costs are important, reducing the plant size while increasing the energy demand is only a partial solution. Laminar Contactors. To overcome this coupling, we need to consider a different mechanism for gas-liquid contacting. If we turn to laminar flow, an external structure should be used to create or maintain the surface area, e.g., in a falling film reactor, the gasliquid area is roughly equal to the wall area. In capillaries at moderate velocities, the predominant flow pattern is called Taylor25 flow (see Figure 1). In Taylor flow, the gas bubbles are too large to retain their spherical shape and are stretched to fit inside the channel. Surface tension pushes the bubble toward the channel wall, and only a thin film remains between the bubble and the wall. The thickness δ of the film is mainly due to viscous stresses near the bubble caps. From a lubrication analysis,26 we find the following for a bubble train moving at a velocity U in a capillary of diameter d:
δ µU ∼ Ca2/3, with Ca ) d γ
(4)
Instead of resisting the breakup into smaller bubbles and, thus, opposing high mass-transfer rates, the surface tension forces minimize the thickness of the film separating the bubble from the catalyst. The liquid is effectively sealed between the bubbles and cannot escape the slug that it forms. This prevents bubble coalescence, and the surface tension forces now eliminate the need for turbulent energy to break up the bubbles. Of course, the small bubbles that enter the channel still have to be created, which still costs energy and which might well be done using a turbulent contactor. The important distinction is that, once inside the channel, no energy is required to maintain the small bubble size. The energy requirement may actually be rather high for a small reactor, with short channels and a relatively large disperser at the entrance of the
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channels. On the other hand, in a reactor with long channels, the energy dissipated in the feed section may be ignored, and the energy requirement is very low. Apart from the power requirement of a gas-liquid disperser, we need energy (1) to force the gas through the column, (2) to force the liquid through the column, and (3) to lift the liquid in the liquid recycle line from the bottom of the column to the top of the column, which yields
(VP) ) (∆pL)
col
(uL,s + uG,s) + FguL,s
(5)
We begin with the simpler analysis of long bubbles and slugs, for which we ignore mass transfer and Laplace pressure terms at the bubble caps. Then, we can simply estimate the pressure drop over the column by
( ) ∆p L
col
[
) L
2Fµ U - Fg d2
]
(6)
Using L ) uL,s/U and U ) uL,s + uG,s, the power input associated with the static head FgL cancels against the power input for lifting the liquid, leaving only a laminar, viscous term to yield
LFµU2 P ∼ V d2
()
(7)
in which F is the Hagen-Poiseuille proportionality constant for developed flow (16 for round channels, 14.2 for square channels, etc.). Still for long bubbles and slugs, we ignore the contribution from the caps to the mass transfer and we estimate the mass transfer from the bubble to the film by penetration theory2
x
kLa ∼ G
DU d2LB
(8)
By introducing the unit cell length LUC ) LB/G and by substituting eq 7, we find a form that allows a comparison with eq 3:
kLa ∼
x
DG
P 1/4 1/2 V dLUC(FµL)
()
(9)
So, for laminar contactors, we predict that the mass transfer is a much weaker function of the amount of energy dissipated than it is for turbulent contactors. The fact that energy is not required for interfacial area generation is in perfect agreement with this scaling analysis. Of course, there still is an impact of velocity on the mass transfer, as a higher velocity reduces the contact times in penetration theory. The group under the root in eq 9 may be estimated for oxygen transfer to an aqueous medium. Using the following estimates for an approximate order of magnitude analysis, D ) O(10-9), d ) O(10-3), LUC ) O(10-2), µ ) O(10-3), and G ) O(10-1), we find that the entire group is O(10-1) and we estimate
kLa ≈ 0.1
(VP)
1/4
(10)
For a low power input, e.g., (P/V) ) 1 kW/m3, this gives kLa ∼ 0.5, which is an order of magnitude higher
Figure 2. Gas-liquid mass transfer versus power input for monoliths and turbulent contactors. All data are for the O2/water system. The dotted line corresponds to eq 10; the shaded area gives the range of kLa vs (P/V) for monoliths. The five larger dots in the monolith data are for a set of experiments where the gas holdup G was kept at 0.6.
than can be obtained in turbulent contactors at the same power input. Again, this result can be understood by realizing that no power is required for bubble breakup. If the bubbles and slugs are short, then the Laplace pressures associated with each bubble become important. Fortunately, this contribution to the pressure drop is of the same order as the frictional losses,1 e.g., F ) 45 for air/water and Lslug ∼ 4d, so we can keep eq 7 with a higher value for F. For short bubbles, we no longer ignore the mass transfer through the caps, which we again estimate using penetration theory2
kLa ∼
x
DU dLUC2
(11)
or by substituting eq 7
k La ∼
x
LUC
2
D P 1/4 1/2 V (FµL)
()
(12)
This shows that, if the unit cell is short, the channel diameter becomes less important, but the bubble length and slug length become more important. The group under the root in eq 12 is similar in value to the group under the root in eq 9 if LUC2 ∼ dLUC or LUC ∼ d, which is consistent with the criterion of short bubbles and slugs for which eq 12 was derived. Because eq 12 only adds to eq 9 in the same order of magnitude, we do not need to change the order-of-magnitude estimate of eq 10. Physical Adsorption of Oxygen In Figure 2, experimental mass-transfer data for the adsorption of oxygen are compared for turbulent contactors and monoliths. The data for stirred tanks and bubble columns follow the trend predicted by eq 3, and the different lines correspond to different values of (uL,s/V). The monolith data were taken from Kreutzer et al.10 Using exactly the same setup, we have also measured the pressure drop, and the data in Figure 2 were obtained by calculating the power input from the experimental pressure drop data. The monolith data are
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consistently higher than the data for the turbulent systems at equal power input. There is significant scatter in the monolith data. The mass transfer was measured at steady state for two lengths of monolith columns. The measured outlet concentration of the short column was used as the inlet concentration for the rest of the longer column, and with the measured outlet concentration, the mass-transfer group was determined from
kLa )
(
)
Csat - Cout,short U ln Llong - Lshort Csat - Cout,long
(13)
Although the oxygen concentration could be determined with an accuracy of 1.5% of the saturation value, the difference Csat - Cout,long was typically less than 0.1Csat, and the subtraction of very similar numbers contributed significantly to the experimental error. Apart from the experimental error, the monolith data in Figure 2 are obtained for 0.3 < G < 0.7. As indicated by eq 9, kLa is a function of G. There is a trend in the data that the higher kLa values in Figure 2 correspond to a higher gas holdup. The five larger symbols in Figure 2 are for G ) 0.6. Also, the parameter F was found to be a strongly nonlinear, nonmonotonic function of the holdup (see ref 27), which makes it impossible to correct for G in a straightforward manner. In Figure 2, we also plotted eq 10, and the order of magnitude, predicted in the section above, is confirmed by the experimental data. Heiszwolf et al17 used a correlation by Bercˇicˇ and Pintar28 and experimental data in a loop reactor where the pressure drop over the column was kept at zero to obtain
kLa ) 7.5 × 10-2
(VP)
0.2
(14)
which is fairly similar to eq 10. Recently, Van Baten and Krishna2 performed a CFD study that demonstrated that the correlation of Bercˇicˇ and Pintar did predict values of the right order of magnitude, but they improved the modeling by introducing the penetrationtheory model that forms the basis of the analysis in this paper. So, although the correlations used for eq 14 are now superseded, the absolute values were based on experiment and still hold. Note that the values of Heiszwolf et al. were slightly lower than the data presented here, which is consistent with the fact that their data were obtained at somewhat lower gas holdups: a forced gas circulation, which does not require too much power, does help to achieve a higher mass transfer. Of course, the choice between the slightly higher mass transfer and the reduced cost of eliminating a fan or compressor in the gas-recirculation is an economical one. Suspended Cell-Culture Bioreactors The analysis presented above suggests that monoliths are ideal for intensifying the contacting in gas-liquid reactors. The most important uncertainty is whether cells attach to the monolith wall and clog the system. As stated in the Introduction, the material properties of cordierite monoliths are probably not ideal to prevent biofilms from attaching to the walls. To test the feasibility of using monoliths, we performed a worst-case feasibility study by using untreated, bare monoliths to grow an aerobic heterotrophic culture. The reactor was
Figure 3. Pressure drop as a measure of biofilm formation at high retention time (HRT ) 30 h).
operated under nonsterile conditions in a loop configuration consisting of a 0.1 m diameter, 0.5 m long monolith column, a 0.007 m3 liquid tank, and a liquid pump. Fresh feed, containing glucose (20 g/L) and minerals, was constantly supplied, and liquid was constantly withdrawn from the system. During operation of the loop reactor, oxygen is consumed by (1) suspended cells and (2) cells in the biofilm on the channel walls. We have monitored the growth of the biofilm by recording the pressure drop over the reactor: an increase in pressure drop indicates increased clogging of channels. The liquid and gas flowrate in the reactor were kept at 1.0 × 10-3 m3/s and 1.15 × 10-3 m3/s, respectively, during the entire experiment. The system is operated as a continuous recycle reactor: liquid entering the system is recycled, on average, many times over the column before it leaves the loop. The most important parameter determining the biofilm growth is the hydraulic retention time (HRT), which is, in chemical engineering terms, the average residence time of the liquid in the entire system. It is important not to confuse the HRT with the recycle time, which is only a few seconds. For a short HRT, the cells in suspension are flushed out of the loop and most of the oxygen transferred in the monolith to the liquid phase is available for the biofilm on the monolith wall. For a long HRT, on the other hand, a high concentration of suspended cells builds up in the loop and these cells compete with the biofilm for dissolved oxygen in the monolith. The second important parameter is the concentration of glucose in the feed. High glucose concentrations lead to high biomass concentrations. As a rule of thumb, we found that each g/L of glucose in the feed yielded 0.5 g of dry biomass per liter of medium. Short Retention Time. When the hydraulic retention time was as low as 30 min, conditions for biofilm formation were very favorable, and within a few hours, a sharp increase in pressure drop indicated extensive biofilm growth for all biomass concentrations and monolith channel sizes. Long Retention Time. We first tested a monolith with 400 cells per square inch of frontal area (400 cpsi or d ) 1.09 mm) and found that, within a few days of operation, the pressure drop increased very fast (see Figure 3). Experiments with a 50 cpsi monolith (d ) 3 mm) were more successful. With a glucose feed of 20 g/L, after 17 days the pressure drop increased very fast,
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Figure 4. Photograph of the biofilm after a 2-week experiment in a 50-cpsi monolith.
indicating clogging. The monolith was removed from the reactor, and the shape of the biofilm was photographed. Figure 4 shows that biofilm formation is delayed in the corners and is most rapid far away from the corners. This may be explained by the fact that a thick meniscus forms in the corners as the bubbles pass by: the lubricating film is thick in the corners, and as a result, the biofilm in the corners is starved from oxygen. After cleaning the monolith, simply by rinsing, the experiment was continued, and essentially the same operating time was obtained; we estimate that, by regular washing of the monolith, long stable operation is possible. In a later experiment, we increased the feed glucose concentration to 40 g/L but kept the HRT at 30 h. This resulted in a more concentrated culture and faster biofilm growth: after 5 days, cleaning was necessary. Immobilized Enzyme Bioreactors So far, we have considered homogeneous catalysis (by suspended cells). The more established gas-liquid application of monoliths involves a heterogeneous catalyst on the wall. The biochemical equivalent is a reactor with an immobilized enzyme on the wall, for which we also consider mass transfer and power input. Figure 1 shows that the liquid is divided into a recirculation region in the slugs and a lubricating layer separating the bubbleslug train from the wall. For the transport of gas to a catalyst on the wall, the film turns out to be the dominant resistance.29,30 In a first approximation, we can assume that the slugs are efficient in transporting gas that dissolves at the bubble caps to the lubricating film, and we obtain an estimate for the mass-transfer coefficient using film theory
kGfS )
D D ∼ δ dCa2/3
(15)
Now the surface tension actively assists in reducing the film resistance to mass transfer, while viscous stresses thicken the films. Substituting eq 7 and using the definition of the Capillary number, we obtain
x 3
kGfSa ∼
D3γ2FL P -1/3 µd8 V
()
(16)
An increase in energy input into the systemsor, put plainly, an increase in the velocity of the bubble trains
Figure 5. Gas-liquid-solid mass transfer in various contactors. The data of Linek et al.23 and Schlu¨ter and Deckwer24 are the G/L mass transfer data also found in Figure 2. The data for the monolith are calculated using δ/d ) 0.66Ca0.66, properties of water and oxygen, D ) 2.8 × 10-9 m2/s, G ) 0.5, and F ) 60. The data from Kreutzer et al.10 were obtained using hydrogen/toluene instead of oxygen/water.
will increase the viscous stresses and deteriorate the mass transfer. This effect (improved mass transfer at lower energy input) seems counterintuitive at first but follows readily from the lubrication analysis. Kreutzer et al.10 demonstrated experimentally using the hydrogenation of R-methylstyrene that, at low velocity, the mass transfer to the wall indeed increased. For a fair comparison to data obtained in conventional bioreactors, it should be noted that the experiments by Kreutzer et al.10 were performed using hydrogen in toluene. For this system, the diffusion coefficient of the dissolved hydrogen is higher than the diffusion coefficient of oxygen in water. We have calculated the mass transfer of oxygen to the wall through an aqueous medium, using 0.66 as the proportionality constant in eq 4 (see, for example, ref 26). Note that the calculated values are for round channels. In coated square channels, the mass-transfer rate is somewhat lower, but the trend (better mass transfer at lower power input) is the same. The experimental bubble column data from Linek et al.23 and the stirred tank data from Schlu¨ter and Deckwer24 are also plotted in Figure 5. If we ignore the shuttling of catalyst particles to the film surrounding bubbles in turbulent contactors, then the highest gasto-solid mass-transfer rate is obtained at high catalyst loading, and in a first approximation, the gas-liquid mass-transfer rate, as defined by eq 3, can be used to estimate the overall mass transfer. Figure 5 highlights the counterintuitive behavior of monoliths: the less energy is introduced, the better the mass transfer. Discussion The analysis of power input and mass transfer in this paper was limited to scaling, and the results serve to demonstate the opportunities that arise when alternatives to the contacting workhorse, turbulence, are considered. The works of Bercˇicˇ and Pintar28 and Van Baten and Kirshna2 have elucidated the most important aspects of G/L mass transfer, and two-phase pressure drop in capillary channels is discussed in detail by Kreutzer et al.;1 however, more experimental mass-
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transfer data is needed, in particular with using different fluids at controlled, independently varied bubble and slug lengths. Although the slug length may be extracted from the experimental pressure drop data,1,16 singlechannel studies will provide data with less experimental error and better control over the slug and bubble length. Nevertheless, the scaling analysis compares quite well with experimental data, and from the scaling analysis, several aspects of monolith loop reactor design may be considered Distributors. The proper distribution of gas and liquid over the column crosssection is crucial for monoliths, because inside a monolith block, no redistribution can occur. In the biofilm growth experiments, we have found that stagnant zones, e.g., due to misalignment of the distributor, provide a starting point for biofilm clogging that can pass to adjacent cells. Also, the present analysis is based on the assumption that the pressure drop in the distributor is not too high. Fortunately, static mixers can be used that combine a good distribution with a low pressure drop.15,31 For a G/L contactor, the distributor should create bubbles and slugs that are short inside the channels, because this improves mass transfer (eq 12) and increases flow stability. For G/L/S reactors with catalyst on the channel walls, the first argument hardly holds, while the stability argument is equally valid as in G/L reactors. Channel Size. Equations 9 and 12 show that the mass transfer is only a mild function of the channel diameter. For this reason, we felt comfortable using lowcpsi monoliths for Taylor flow loop-reactor applications where clogging may occur. If dust or clogging tolerance is important, it seems worthwhile to sacrifice some interfacial area. On the other hand, for G/L/S reactors, the channel size is crucial, and channel size should be increased only as a last resort. Gas and Liquid Throughput. The G/L/S mass transfer improves with lower throughput, so it makes sense to operate at the lowest possible practical flowrates. The lower limit is set (1) by the requirement of Taylor flow, for which 2-3 cm/s is enough for the smaller channels (>200 cpsi) and (2) by the requirement of stable gas/liquid flow, which may require somewhat higher flowrates.15 The ratio of gas to liquid throughput hardly affects the mass-transfer rate, but a sizable gas holdup may be required if entire bubbles may otherwise be completely dissolved, resulting in the loss of the Taylor flow characteristics. The G/L mass transfer scales only with (P/V)1/4, and increasing or decreasing the flow rate has a limited effect on the mass transfer. For most applications, it seems best to be just above the lower limit for stable operation.
turbulent contactors. This flow pattern can be used for biochemical conversions using cell cultures, provided the channels are not too small and the operating conditions are such that biofilm formation is suppressed. If the segmented flow pattern is used for a reaction catalyzed at the walls of the capillary channels, then the mass transfer is actually improved by reducing the amount of energy that is dissipated in the system. This allows the simultaneous achievement of two goals of process intensification: reduction of the energy requirement and reduction of equipment size. Acknowledgment This work was financially supported by grant DST 66.4653 of the Dutch Foundation for Technological Science (STW-NWO). Notation a ) interfacial area, m2/m3 d ) diameter, m D ) diffusion coefficient, m2/s g ) gravitational constant, m/s2 k ) mass-transfer coefficient, m/s L ) length, m p ) pressure, Pa P ) power, W u ) velocity, m/s U ) sum of gas and liquid superficial velocity, m/s V ) volume, m3 Greek Letters γ ) surface tension, N/m ˜ ) holdup µ ) viscosity, (Pa s) F ) density, kg/m3 Dimensionless Groups Ca ) Capillary number ()µU/γ) f ) friction factor F ) laminar friction constant ()fRe) Re ) Reynolds number ()FUd/µ) We ) Weber number ()FU2d/γ) Subscripts B ) bubble Ca ) capillary scale G ) gas L ) liquid s ) superficial S ) slug TP ) two phase UC ) unit cell, i.e., a bubble and a slug
Literature Cited Conclusions In this paper, we have proposed the use of capillary channels in general, and monoliths in particular, to intensify processes involving gas-liquid mass transfer. We have focused on bioreactors, but the behavior of the monolith is easily translated to conventional gas-liquid(-solid) reactors. Using a simple scaling analysis, involving (1) viscous pressure drop, (2) hydrostatic pressure drop, (3) interfacial pressure drop, and (4) penetration theory for mass transfer, it has been demonstrated that two-phase laminar bubble-train flow in small channels can exhibit better mass transfer for a given power input than
(1) Kreutzer, M. T.; Kapteijn, F.; Moulijn, J. A.; Kleijn, C. R.; Heiszwolf, J. J. Inertial and interfacial effects on the pressure drop of Taylor flow in capillaries. AIChE J. 2005, in press. (2) Van Baten, J. M.; Krishna, R. CFD simulations of mass transfer from Taylor bubbles rising in circular capillaries. Chem. Eng. Sci. 2004, 59, 2535-2545. (3) Vandu, C.; Ellenberger, J.; Krishna, R. Hydrodynamics and mass transfer in an upflow monolith loop reactor. Chem. Eng. Prog. 2005, 44, 363-374. (4) Boger, T.; Roy, S.; Heibel, A. K.; Borchers, O. A monolith loop reactor as an attractive alternative to slurry reactors. Catal. Today 2003, 79-80, 441-451. (5) Boger, T.; Heibel, A. K.; Sorensen, C. M. Monolithic catalysts for the chemical industry. Ind. Eng. Chem. Res. 2004, 43 (16), 4602-4611.
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Received for review March 1, 2005 Revised manuscript received April 29, 2005 Accepted May 3, 2005 IE050286M
